Solution of 2-D Electromagnetic Problems for Inhomogeneous Objects using 1-D FFT

Document Type : Research Paper

Authors

1 Electrical Engineering Dept., Yazd University, Yazd, Iran

2 Department of Electrical Engineering Yazd University,Yazd,Iran

Abstract

This paper presents a novel solution of two dimensional (2-D) method of moments (MoM) in Cartezian coordination to calculate the source-type electric field integral equations (EFIE) arising from electromagnetic inverse scattering problems in microwave imaging (MI). The main issue is to reduce the 2-D problem into 1-D case, using decomposition the electric-type Green’s function of inhomogeneous media. In this regard, recursive formulas in spatial frequency domain are derived for both TE and TM problems and the scattering field is rewritten into upward and downward components in a recursive form. It helps us to calculate a 2-D problem using 1-D stabilized biconjugate-gradient fast Fourier transform (BCGSFFT) of the induced source and save lots of memory and time for inhomogeneous objects in MI performance. The paper provides 2-D TM and TE scattering examples for different scenarios and compares the proposed and conventional algorithms to demonstrate merits of the proposed formulas in terms of the accuracy and computational efficiency.

Keywords


1- H. Liu, Z. Q. Zhang, T. T. Wand, J. A. Bryan, G. A. Ybarra, L. W. Nolte, and W. T. Joines, “Active microwave maging. I. 2-D forward and inverse scattering methods,” IEEE Trans. Microwave Theory Tech., vol. 50, no. 1, pp. 123-133, Jan. 2002.
2- Salucci, G. Oliveri and A. Massa, “GPR prospecting through an inverse scattering frequency-hopping multi-focusing approach,” IEEE Trans. Geosci. Remote Sens, vol. 53, no. 12, pp. 6573-6592, Dec. 2015.
3- Zhang, J. Meng, L, Sun, X, Zhang and S, Shu, “Performance Analysis of Internal Solitary Wave Detection and Identification Based on Compact Polarimetric SAR,” IEEE Access, vol. 8, pp. 172839-172847, Sep. 2020.
4- Salucci, L. Poli, N. Anselmi and A. Massa, “Multi-frequency particle swarm optimization for enhanced multiresolution GPR microwave imaging,”IEEE Trans. Geosci. Remote Sens., vol. 55, no. 3, pp. 1305-1317, March 2017.
5- Sabzevari, R. Winter, D, Oloumi and K. Rambabu, “A Microwave Sensing and Imaging Method for Multiphase Flow Metering of Crude Oil Pipes,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 13, pp. 1286-1297, Mar. 2020.
6-Kharkovsky, A.C. Ryley, V. Stephen and R. Zoughi, “Dual-polarized near-field microwave reflectometer for noninvasive inspection of carbon fiber reinforced polymer-strengthened structures,” IEEE Trans. Instrum. Meas, vol. 57, no.1, pp.168-175, Jan. 2008.
7- Giri and S. Kharkovsky, “Dual-laser integrated microwave imaging system for nondestructive testing of construction materials and structures,”IEEE Trans. Instrumentation and Measurement, vol. 67, no. 6, pp. 1329-1337, June 2018.
8- J. Liu, Z.Y. Xu, J.L. Wei et al., “Experimental study on microwave radiation from deforming and fracturing rock,”IEEE Geosci. Remote Sens, vol. 54, no. 9, pp. 5578-5587, Sept. 2016.
9- Massa et al., “A microwave imaging method for NDE/NDT based on the SMW technique for the electromagnetic field prediction,” IEEE Trans. Instrumentation and Measurement, vol. 55, no. 1, pp. 240-147, Feb. 2006.
10- T. Case, M. T. Ghasr and R. Zoughi, “Nonuniform Manual Scanning for Rapid Microwave Nondestructive Evaluation Imaging,”IEEE Trans. Instrumentation and Measurement, vol. 62, no. 5, pp. 1250-1258, May 2013.
11- D. Carrigan, B. E. Forrest, H. N. Andem, K. Gui, L. Johnson, J. E. Hibbert, et al., “Nondestructive testing of nonmetallic pipelines using microwave reflectometry on an in-line inspection robot,”IEEE Trans. Instrumentation and Measurement., vol. 68, no. 2, pp. 586-594, Feb. 2019.
12- K. Amineh, M. Ravan and R. Sharma, “Nondestructive Testing of Nonmetallic Pipes Using Wideband Microwave Measurements,” IEEE Trans. Microwave Theory and Techniques, vol. 68, no. 5, pp. 1763-1772, May 2020.
13- Rahman, A. Haryono, Z. Akhter and M. Abou-Khousa “On the Inspection of Glass Reinforced Epoxy Pipes using Microwave NDT,” IEEE Intern. Instrumentation and Measurement Technology Conference (I2MTC), May 2019.
14- Gholipur, M. Nakhkash, “A data focusing method for microwave imaging of extended targets,” Journal of Communication Engineering, vol. 7, no. 1, Jan.-June 2018.
15- Pastorino, Microwave Imaging, New York: Wiley, 2010,ch 4, pp. 57-78.
16- M. Xu, Q. H. Liu and Z. Q. Zhang, “The stabilized biconjugate gradient fast Fourier transform method for electromagnetic scattering,” Appl. Computational Electromagnetic Soc. Jour., vol. 17, pp. 97-103, 2002.
17- Joachimowicz, C. Pichot and J.P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag., vol. 39, no. 12, pp. 1742-1753, Dec. 1991.
18- Konakyeri Arıcı and A. Yapar, “Numerical Calculation of 2-D Inhomogeneous Media Green’s Function and Some Applications in Electromagnetic Scattering Problems,” IEEE Trans. Antennas Propag., vol. 67 , no. 1, pp. 369-377, Jan. 2019.
19- Q. Zhang and Q. H. Liu, “Three-dimensional weak-form conjugate and biconjugate-gradient FFT methods for volume integral equations,” Microwave Opt. Technol. Lett., vol. 29, no. 5, pp. 350-356, June 2001.
20- Q. Zhang, Q. H. Liu, C. Xiao, E. Ward, G. Ybarra and W. T. Joines, “Microwave breast imaging: 3-D forward scattering simulation,” IEEE Trans. Biomedical Eng., vol. 50, no. 10, pp. 1180-1189, Oct. 2003.
21- C. Chew, Waves and Fields in Inhomogeneous Media, Wiley-IEEE Press, New York, 1999.
22- Gao, C. Torres-Verdin and T. M. Habashy, “Analytical techniques to evaluate the integrals of 3D and 2D spatial dyadic Green's functions,” Prog. Electromag. Research (PIER), vol. 52, pp. 47-80, 2005.